6 ms·

How Math Might Reveal Quantum Gravity

68 points by doctoboggan 5y ago

benlivengood 5y ago
Now I'm curious; which parts of quantum field theory don't have a rigorous basis? EDIT: https://physics.stackexchange.com/questions/6530/rigor-in-quantum-field-theory https://physics.stackexchange.com/questions/6530/rigor-in-qu... is pretty informative.
- spekcular 5y ago
  Basically all of it. No one has rigorously constructed a non-trivial quantum field theory in four dimensions (the physically realistic case; 3 spatial + 1 time). I am also much more pessimistic than Seiberg about the possibility that a priori mathematical investigation is going to say something useful about quantum gravity. The following essay gives a pessimistic point of view on a particular program to rigorize QFT, but the arguments generalize: http://philsci-archive.pitt.edu/8890/ http://philsci-archive.pitt.edu/8890/. But, that's a long paper. For a super-condensed take on why the project might be hopeless, read section two of this paper: http://philsci-archive.pitt.edu/15296/1/qm-continuum%20revised.pdf http://philsci-archive.pitt.edu/15296/1/qm-continuum%20revis....
foxes 5y ago
Writing down a field theory is seems to be writing out a path integral of some sort: \int Dx Exp[S[x]] Where \int Dx is like a sum, x is a field (a thing that assigns numbers or an object to a point in space), Exp[S[x]] is a weighting. You sum over all possible field configurations weighted by S[x], which is called the action. You can feed in other fields to this sum and calculate expectations of events happening, a bit like a Fourier transform or Gaussian integral from statistics. Classical configurations (classical paths/trajectories) this is the biggest contribution, then all the quantum stuff gets weighted less. Formalising this notion is complicated for the sorts of objects and spaces needed in physics. This is also problematic when it comes to quantising general relativity, the gravitational field in a sense is not just a field on space, it's more like space itself, although you can try to describe that as a field. People get around this by summing over geometry. In a sense you can test what the geometry is by seeing what it does to objects, maybe a bit like forcing particles to interact with each other and seeing what gets produced says something about internal structure. It is interesting of course that we try and use classical information plus some choices to build a field theory. In my opinion it is sort of unnatural to quantise, you are making choices. Broadly quantisation is sticking some commutative theory in a non commutative theory. But since we know the universe actually runs on those quantum rules, seems wrong to define it as like the embedding of a classical theory, it should go the other way, classical information should emerge naturally instead. Perhaps the other issue is that field theories are effective in a sense. Much like fluid dynamics doesn't say anything about the internal molecular composition of water, fields are an effective theory. Perhaps string theory tries to get around this by having large scale dynamics and then saying what the micro local structure is, but that is even less of a well defined notion than a QFT.
ncmncm 5y ago
There is no mathematical necessity for physical things that are equal to be equal in general. We have only the one universe. Things we seem to find equal need to be mathematically permitted to be equal, within the tolerance we can measure, but it need not be mathematically required. Unifying gravitation and quantum mechanics amounts to asserting an equality we can never check because the numbers are tens of orders of magnitude too small to measure. People chasing unification have left off doing physics, because they have abandoned experiment. There is nothing wrong with engaging in maths for maths' sake; just don't call it physics. There are whole worlds of physics still barely touched, because the maths have been too hard. There are plenty of open questions in solid state phenomena, in plasma fluid dynamics, in relativistic dynamics, and even in ordinary fluid dynamics.
- eigenket 5y ago
  I disagree with this basically completely. In quantum physics labs around the world we put things in superpositions of being in different positions all the time, mainly we do it with photons and electrons, but people are doing it with larger objects as well. We essentially have absolutely no fucking clue what is happening to the gravitational field when an object is in a super position of being in to different places. It definitely does something when an electron is in a superposition of different places and no one in the world can tell you what. That is the point of unification - not some wild mathematical goosechase - we know quantum effects can do stuff to gravity (and vice-versa) and no one knows what is going on. The last sentence of comment is reasonably true, but a lot of very, very smart people are working on all of those fields, its not like they're gonna stop because other people are working on quantum gravity.
  - ncmncm 5y ago
    Fine, you have told us about something we already knew about. How do you propose to detect the gravitational field of a superposed electron? Or even a proton, 1836 times more massive? Or even a U nucleus, 4.4M times more massive? The number of positions for post-docs in physics departments is capped by department budgets. Each seat given to a pure mathematician masquerading as a physicist is a seat not available to one who would rather do, you know, physics. If, someday, it became possible to make progress on the topic, actual physicists would jump at the chance. Without possibility of an experiment, it is just maths. Maths departments welcome that, but don't get physics department budgets. For reasons.
miika 5y ago
https://hiup.org/publications/ https://hiup.org/publications/ They claim to have found a simple solution. Looks like Planck’s length was turned into a sphere, then they calculated how many of those spheres would fit inside a single proton. That was compared against how many Planck circles would fit on surface of single proton. From the ratio of the two they could solve size and critical mass of the universe, by looking at single proton. Quite amazing if that’s true. They think proton is a mini black hole and when it’s scaled up to size of the universe things match. And key to nailing it in the end was to consider volumes made from intersecting spheres (like flower of life pattern) instead of tiled cubes. The guy behind this certainly faced lot of criticism before but apparently now the math works. Anyways I don’t have skills to evaluate this by myself but maybe it’s worth checking out by someone who can do the math. Don’t shoot the messenger ok :)
- radioactivist 5y ago
  That paper is not anything really. Their "formula" for the electron mass is a combination of some Planck units the fine structure constant and the Bohr radius. But the Bohr radius is defined in terms of the electron mass -- and if you put in the usual expressions it looks like everything else cancels. So the agreement appear to be entirely by construction, they've basically just mathematically obsfucated the input (the electron mass).
drran 5y ago
Will math answer the question: what releases energy, when two objects are attracted by gravitation, and what stores energy, when we pull them apart?
- rnhmjoj 5y ago
  This is not something particular to gravity: you can ask the same in EM and any other classical field theory, I think. You can compute the amount of energy, but where is the energy stored is not well-defined: you can either think it's stored in the masses (or charges, currents, etc.) or in the fields without contradictions.
  - radioactivist 5y ago
    This is true, though there is there is one strong philosophical reason to prefer accounting for the energy as being stored in the fields themselves: it makes the theory "local". I.e. for energy to go from A to B it's got to travel the distance between them (it does this through the fields). The idea locality is a central part of relativity and for this reason theories that are explicitly local (i.e. have fields to carry energy, momentum, etc) rather than implicitly local (have apparent action at a distance) are preferred.
    - drran 5y ago
      "Field" is mathematical terminology, a 3D array of values. What is represented by a mathematical field in the physical world? Is the gravitational field a gas, ideal fluid, solid, crystal, or plasma? (IMHO, it's ideal fluid). What causes it to release energy when two objects are attracted? Of course, it goes from higher energy state into lower energy state, but what state it is? What causes attraction? It's because there is a gradient in the ideal fluid around every object, or because it's a form of interaction between particles of objects, or it's a something global, e.g. shadow, which blocks background radiation causing imbalance? (Non-native speaker).
      - radioactivist 5y ago
bronzeage 5y ago
It's obvious that the universe is something that's at least Turing complete. Turing machines have a very specific scale of a single "cell" in space and a single "time step" in time, and describing them in a "scale invariant" way is intractable problem because of the halting problem. Minewhile physicists are insisting on having scale invariant descriptions. That's obviously doomed to fail. Then there's the lattice idea, which fails because if your universe only has 6 directions, like a lattice, getting the lattice infinitely small will never change the metric from L1 to L2. How do you get normal euclidean metric from something discrete is the first question to ask.

68 points by doctoboggan 5y ago

Now I'm curious; which parts of quantum field theory don't have a rigorous basis? EDIT: https://physics.stackexchange.com/questions/6530/rigor-in-quantum-field-theory https://physics.stackexchange.com/questions/6530/rigor-in-qu... is pretty informative.

spekcular 5y ago
Basically all of it. No one has rigorously constructed a non-trivial quantum field theory in four dimensions (the physically realistic case; 3 spatial + 1 time). I am also much more pessimistic than Seiberg about the possibility that a priori mathematical investigation is going to say something useful about quantum gravity. The following essay gives a pessimistic point of view on a particular program to rigorize QFT, but the arguments generalize: http://philsci-archive.pitt.edu/8890/ http://philsci-archive.pitt.edu/8890/. But, that's a long paper. For a super-condensed take on why the project might be hopeless, read section two of this paper: http://philsci-archive.pitt.edu/15296/1/qm-continuum%20revised.pdf http://philsci-archive.pitt.edu/15296/1/qm-continuum%20revis....

foxes 5y ago

Writing down a field theory is seems to be writing out a path integral of some sort: \int Dx Exp[S[x]] Where \int Dx is like a sum, x is a field (a thing that assigns numbers or an object to a point in space), Exp[S[x]] is a weighting. You sum over all possible field configurations weighted by S[x], which is called the action. You can feed in other fields to this sum and calculate expectations of events happening, a bit like a Fourier transform or Gaussian integral from statistics. Classical configurations (classical paths/trajectories) this is the biggest contribution, then all the quantum stuff gets weighted less. Formalising this notion is complicated for the sorts of objects and spaces needed in physics. This is also problematic when it comes to quantising general relativity, the gravitational field in a sense is not just a field on space, it's more like space itself, although you can try to describe that as a field. People get around this by summing over geometry. In a sense you can test what the geometry is by seeing what it does to objects, maybe a bit like forcing particles to interact with each other and seeing what gets produced says something about internal structure. It is interesting of course that we try and use classical information plus some choices to build a field theory. In my opinion it is sort of unnatural to quantise, you are making choices. Broadly quantisation is sticking some commutative theory in a non commutative theory. But since we know the universe actually runs on those quantum rules, seems wrong to define it as like the embedding of a classical theory, it should go the other way, classical information should emerge naturally instead. Perhaps the other issue is that field theories are effective in a sense. Much like fluid dynamics doesn't say anything about the internal molecular composition of water, fields are an effective theory. Perhaps string theory tries to get around this by having large scale dynamics and then saying what the micro local structure is, but that is even less of a well defined notion than a QFT.

ncmncm 5y ago

There is no mathematical necessity for physical things that are equal to be equal in general. We have only the one universe. Things we seem to find equal need to be mathematically permitted to be equal, within the tolerance we can measure, but it need not be mathematically required. Unifying gravitation and quantum mechanics amounts to asserting an equality we can never check because the numbers are tens of orders of magnitude too small to measure. People chasing unification have left off doing physics, because they have abandoned experiment. There is nothing wrong with engaging in maths for maths' sake; just don't call it physics. There are whole worlds of physics still barely touched, because the maths have been too hard. There are plenty of open questions in solid state phenomena, in plasma fluid dynamics, in relativistic dynamics, and even in ordinary fluid dynamics.

eigenket 5y ago
I disagree with this basically completely. In quantum physics labs around the world we put things in superpositions of being in different positions all the time, mainly we do it with photons and electrons, but people are doing it with larger objects as well. We essentially have absolutely no fucking clue what is happening to the gravitational field when an object is in a super position of being in to different places. It definitely does something when an electron is in a superposition of different places and no one in the world can tell you what. That is the point of unification - not some wild mathematical goosechase - we know quantum effects can do stuff to gravity (and vice-versa) and no one knows what is going on. The last sentence of comment is reasonably true, but a lot of very, very smart people are working on all of those fields, its not like they're gonna stop because other people are working on quantum gravity.
- ncmncm 5y ago
  Fine, you have told us about something we already knew about. How do you propose to detect the gravitational field of a superposed electron? Or even a proton, 1836 times more massive? Or even a U nucleus, 4.4M times more massive? The number of positions for post-docs in physics departments is capped by department budgets. Each seat given to a pure mathematician masquerading as a physicist is a seat not available to one who would rather do, you know, physics. If, someday, it became possible to make progress on the topic, actual physicists would jump at the chance. Without possibility of an experiment, it is just maths. Maths departments welcome that, but don't get physics department budgets. For reasons.

miika 5y ago

https://hiup.org/publications/ https://hiup.org/publications/ They claim to have found a simple solution. Looks like Planck’s length was turned into a sphere, then they calculated how many of those spheres would fit inside a single proton. That was compared against how many Planck circles would fit on surface of single proton. From the ratio of the two they could solve size and critical mass of the universe, by looking at single proton. Quite amazing if that’s true. They think proton is a mini black hole and when it’s scaled up to size of the universe things match. And key to nailing it in the end was to consider volumes made from intersecting spheres (like flower of life pattern) instead of tiled cubes. The guy behind this certainly faced lot of criticism before but apparently now the math works. Anyways I don’t have skills to evaluate this by myself but maybe it’s worth checking out by someone who can do the math. Don’t shoot the messenger ok :)

radioactivist 5y ago
That paper is not anything really. Their "formula" for the electron mass is a combination of some Planck units the fine structure constant and the Bohr radius. But the Bohr radius is defined in terms of the electron mass -- and if you put in the usual expressions it looks like everything else cancels. So the agreement appear to be entirely by construction, they've basically just mathematically obsfucated the input (the electron mass).

drran 5y ago

Will math answer the question: what releases energy, when two objects are attracted by gravitation, and what stores energy, when we pull them apart?

rnhmjoj 5y ago
This is not something particular to gravity: you can ask the same in EM and any other classical field theory, I think. You can compute the amount of energy, but where is the energy stored is not well-defined: you can either think it's stored in the masses (or charges, currents, etc.) or in the fields without contradictions.
- radioactivist 5y ago
  This is true, though there is there is one strong philosophical reason to prefer accounting for the energy as being stored in the fields themselves: it makes the theory "local". I.e. for energy to go from A to B it's got to travel the distance between them (it does this through the fields). The idea locality is a central part of relativity and for this reason theories that are explicitly local (i.e. have fields to carry energy, momentum, etc) rather than implicitly local (have apparent action at a distance) are preferred.
  - drran 5y ago
    "Field" is mathematical terminology, a 3D array of values. What is represented by a mathematical field in the physical world? Is the gravitational field a gas, ideal fluid, solid, crystal, or plasma? (IMHO, it's ideal fluid). What causes it to release energy when two objects are attracted? Of course, it goes from higher energy state into lower energy state, but what state it is? What causes attraction? It's because there is a gradient in the ideal fluid around every object, or because it's a form of interaction between particles of objects, or it's a something global, e.g. shadow, which blocks background radiation causing imbalance? (Non-native speaker).
    - radioactivist 5y ago

bronzeage 5y ago

It's obvious that the universe is something that's at least Turing complete. Turing machines have a very specific scale of a single "cell" in space and a single "time step" in time, and describing them in a "scale invariant" way is intractable problem because of the halting problem. Minewhile physicists are insisting on having scale invariant descriptions. That's obviously doomed to fail. Then there's the lattice idea, which fails because if your universe only has 6 directions, like a lattice, getting the lattice infinitely small will never change the metric from L1 to L2. How do you get normal euclidean metric from something discrete is the first question to ask.